# Gravity not being a Force

1. Oct 8, 2008

### Mr.Waka

Hello, What a great forum btw.

Im in physics I right now in college. Im going in for my Aerosapce Engineering degree. Most of this stuff is what I did in high school so its not that hard. But when we go into forces my professor made the point that gavity is not a force. In fact he is true that its an acceleration.

So my question to everyone is what is gravity then. I know that gravity is considered one of the fundamental forces of nature, and thats its the weakest of them all, but if a force is considered the mass times acceleration how is gravity a force.

2. Oct 8, 2008

### atyy

Gravity is a force.

GMm/r2=ma

The entire LHS is gravity, which is an interaction between two masses, M and m. It is not the action of one mass on another. If the LHS m were zero, there would be no gravitational attraction between the two masses. It is an interesting quirk that m also enters the RHS.

When the mass M is very large, we can pretend that it is not affected by the gravitational interaction, so it doesn't move. In this approximation, the smaller "test" mass moves in the gravitational field of the stationary larger mass, and gravity is an acceleration.

3. Oct 8, 2008

### Gear300

We're not too sure about gravity. Instead of a force, it could be the curvature in space-time making it seem like a force. Then again, you might ask what adheres matter to space-time (why doesn't it fly out), which might imply something deeper about gravity. It could, at the same time, be a particle...there is much theory to it.

4. Oct 9, 2008

### rcgldr

Some claim that gravity is a fictional force simply because it's relative to mass. Inertial reaction forces to acceleration are also relative to mass of the object being accelerated, for example centerifugal force, and reaction forces are considered to be fictitious forces. In my opinion, even if gravity shares one apect of a fictional force, that's not enough to state that it is a fictional force.

Gravity is an attractive force, similar to an attractive force between oppositely charged particles (except gravity is relative to mass, while an eletrical field is relative to charge). Gravity may have other effects like curving space, and affects the rate at which time passes, but these don't exclude force as a component of gravity. Then again, why call these non-force related properties as properties related to gravity, as opposed to properties of mass?

Last edited: Oct 9, 2008
5. Oct 9, 2008

### Phrak

I think Mr. Waka has walka. But what his physics professor is talking about, I'm sure, is the description of gravity in general relativity. Objects are free of forces when they are feely falling.

What does freely falling mean?

It simply means that a particle follows a geodesic, the equivalent of a straight line in curved spacetime.

A geodesic is the line traced out when a vector in spacetime is displaced, incrementally, in the direction it points. What it means to displace this vector is a little ambiguous, but one condition is that a chosen metric doesn't change with the dispacement.

What's a metric? A metric is what is used to make the Pythagorean theorum work out in curved spacetime, or curvalinear coordinates like polar corrdinates, so that instead of ds^2 = dx^2 + dy^2, you have cross terms. for instance ds^2 = dx^2 + (1/2)dxdy + dy^2.

This is studying relativity backwards, of course. First you lean about the metric, then parallel transportin a vector, then geodesics, then what feely falling means. Of course, Einstein began with freely falling. hm...

Last edited: Oct 9, 2008
6. Oct 9, 2008

### D H

Staff Emeritus
Mr. Waka, The answer to your question depends on your point of view. Since you posted your question in the Classical Physics section of this forum, the answer is that gravity is a force. Had you asked the exact same question in the Relativity section, the answer would have been that gravity is a pseudo force.

That isn't the only common characteristic. Accelerometers don't sense centrifugal force or coriolis force, and they don't sense the acceleration due to gravity. From the classical mechanics POV where gravitation is a real force, it is the only real force that accelerometers can't sense. From the relativistic POV where gravitation is a pseudo force, accelerometers sense the acceleration resulting from all real forces acting on an object.

7. Oct 9, 2008

### Phrak

I don't get it. Just the other day I put my accelerometer in a centrifuge and it read 5g's.

8. Oct 9, 2008

### D H

Staff Emeritus
Your accelerometer registered a 5g acceleration inward: centripetal acceleration.

9. Oct 9, 2008

### rcgldr

10. Oct 9, 2008

### D H

Staff Emeritus
In other words, an accelerometer at rest on the Earth's surface will indicate an upward acceleration of 1g. An accelerometer measures all real forces acting on an object. The forces acting on object at rest on the surface of the Earth are gravitation, pulling it downward, and the normal force, pushing it upward. An eccelerometer doesn't sense the acceleration due to gravity but does sense the acceleration due to the normal force.

On the other hard, an accelerometer located at the center of mass of a space vehicle undergoing free drift in low Earth orbit will measure a near zero acceleration, even though the acceleration due to gravity is about 0.9g. All the space-borne accelerometer senses is the aerodynamic drag on the vehicle. It does not sense the acceleration due to gravity.

11. Oct 9, 2008

### rcgldr

I missed the point about not sensing acceleration (as opposed to force) applied by gravity.

My point is that accelerometers measure the net force on objects inside the accelerometer, and correlate this into acceleration. Gravity is sensed as a force acting upon the objects inside the accelerometer, which is why they indicate 1g when at rest on the earth's surface.

12. Oct 9, 2008

### schroder

g = G M/ r^2 which is an acceleration.
So g is the acceleration due to gravity. If your instructor is referring to g then he is correct in saying that it is acceleration rather than a force.
However, the force of gravity is Fg = G M m/ r^2 and this is definitely a Force, since it is g multiplied by an additional mass, as in F = ma.
So gravity can be considered as either an acceleration, when only the acting mass is considered, or it can be considered as a force, when both the acting mass and the acted on mass are considered. There really is no need for a debate on this issue as all that is required is to clearly state the expression being used.

13. Oct 9, 2008

### D H

Staff Emeritus
You are assuming Newtonian physics here. Fext=ma is true only in an inertial frame. One has to invent fictitious forces to add to the external force to make F=ma appear to be true in a non-inertial frame. One place where Newtonian mechanics differs from general relativity is the concept of an inertial reference frame. In Newtonian mechanics, an inertial frame is some reference frame whose origin is moving at a constant velocity relative to and whose axes are not rotating with respect to some other inertial frame.

In general relativity, an inertial frame is some neighborhood (inertial frames do not have infinite extent in GR) of a point that is following a geodesic in spacetime -- in other words, a finite region in the vicinity of a free-falling point mass of miniscule mass. An accelerometer located at the origin of the inertia frame will measure zero acceleration. The size of the inertial frame depends on how good your accelerometer is.

Gravity is obviously not a force in GR, and I suspect thaat this is the concept to which the instructor was alluding.

14. Oct 9, 2008

### Andrew Mason

I don't necessarily disagree with anything posted above. It is a semantic argument whether gravity is a "force". It produces acceleration of matter so in that sense it is a force. But as a force it is unlike any other since it produces no inertial effects. A mass in free fall acceleration in a gravitational field is equivalent locally to an inertial frame of reference. A mass at rest in a gravitational field is equivalent locally to an accelerating frame.

But you may wish to challenge your teacher using Einstein's own words:"Unified Field Theory". By definition a field is an area where a force applies. He spent most of his adult life trying to develop such a theory in the belief that it was possible to treat the four forces of nature: gravitational, electomagnetic, nuclear (strong and weak) as different aspects of the same phenomenon.

AM

15. Oct 9, 2008

### Gear300

yeah...he wanted an elegant symmetry between the fundamental forces

16. Oct 9, 2008

### Phrak

You say semantics, I say theory. Some of this unification effort was inspired by a letter from Kaluza who was attemping a unification of gravity with electromagnetism by incorporating the 4-potential into a 5 dimensional metric. That is, A_mu = g_{4 mu}. It would be an injustic to appy your definition of a force. It was hoped, electromagnetism as force due to a field impressed upon spacetime, would be replaced by a description of the shape of the hyperspace.

17. Oct 12, 2008

### Naty1

Your prorfessor is right that gravity should not be thought of as a force, rather an acceleration. G, the universal gravitational constant is the cause of the gravitational force but is different from g which is a vector and has units of acceleration.

F = MA =Mg = W In relativity, Einstein determined via his equivalence principle that intertial mass and gravitational mass were equivalent; acceleration is indistinguishable from gravity. Hence in the simple equation above general acceleration A can be equated to gravitational acceleration g to result in a force (weight).